Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces

Notes on Compact Riemann Surfaces

Introduction to Compact Riemann Surfaces

The theory of Riemann surfaces is a classical field of mathematics where geometry and analysis play equally important roles. The purpose of these notes is to present some basic facts of this theory to make this book more self contained. In particular we will deal with classical descriptions of Riemann surfaces, Abelian differentials, periods on Riemann surfaces, meromorphic functions, theta fun...

Generalized Riemann minimal surfaces examples in three-dimensional manifolds products

In this paper, we construct and classify minimal surfaces foliated by horizontal constant curvature curves in M × R, where M is H, R or S. The main tool is the existence of a so called ”Shiffman” Jacobi field which characterize the property to be foliated in circles in these product manifolds.

Protecting Surfaces Using One-Dimensional Nanostructures

Ultraviolet waves, because of their short wavelength, have a high energy and considerable damaging effects on surfaces. Protection against ultraviolet radiations is one of the finishing treatments done on surfaces exposed to sunlight. The importance of this issue in relation to human health, due to complications such as skin burns and cancer, is doubled. Up t...

Isometry Groups of Compact Riemann Surfaces

We explore the structure of compact Riemann surfaces by studying their isometry groups. First we give two constructions due to Accola [1] showing that for all g ≥ 2, there are Riemann surfaces of genus g that admit isometry groups of at least some minimal size. Then we prove a theorem of Hurwitz giving an upper bound on the size of any isometry group acting on any Riemann surface of genus g ≥ 2...